Push-forwards in oriented cohomology theories of algebraic varieties, by Ivan Panin and Alexander Smirnov

Notions of a cohomology theory and an oriented cohomology theory for algebraic varieties are introduced, push-forwards for projective morphisms are constructed and a Riemann-Roch theorem for ring operations between oriented theories is proved. An explicit formula for the Todd genus related to a ring operation is given. The theory is illustrated by motivic cohomology, algebraic K-theory, algebraic cobordism theory and by other examples.

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